Show that two surfaces intersect orthogonally at a point P

Feb 2013
58
0
Calgary
I was given this question to take home and practice but we have not been shown anything like this before and there in nothing in the text like this either. If anyone has any tips on how to start this question I would really appreciate it.

Two surfaces are said to intersect orthogonally at a point P if their
tangent planes are perpendicular at the point P. Show that the surfaces z = (x^2)y and
y = 1/4x^2 + 3/4 intersect orthogonally at (1; 1; 1).

Thanks
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Are you taking Calculus? This is a pretty standard Calculus problem. As you say "Two surfaces are said to intersect orthogonally at a point P if their
tangent planes are perpendicular at the point P." Are you saying you do not know how to find the tangent planes? That is also a pretty basic Calculus problem- similar to "find the tangent line to a curve" that is pretty much the first thing you learn in Calculus!

But even simpler is the fact that two planes are perpendicular (and so the surfaces are perpendicular) if and only if their normal vectors are perpendicular. What are the normal vectors to \(\displaystyle z= x^2y\) and \(\displaystyle y= (1/4)x^2+ 3/4\) at (1, 1, 1)?
 
Feb 2013
1
0
Canada
I think Iytwynk would appreciate the help even more with out the condescending tone......just saying
 
Feb 2013
58
0
Calgary
Thanks for the help but we just covered this section today in class so I was able to get the problem.